Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - 4.5 Exercises - Skill Practice - Page 270: 34


Answer: C

Work Step by Step

$ 3(x+2)^{2}+4=13\qquad$ ...add $-4$ to each side. $ 3(x+2)^{2}+4-4=13-4\qquad$ ...simplify. $ 3(x+2)^{2}=9\qquad$ ...divide each side with $3$. $(x+2)^{2}=3\qquad$ ...take square roots of each side. $\sqrt{(x+2)^{2}}=\sqrt{3}\qquad$ ...simplify. ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $ x+2=\pm\sqrt{3}\qquad$ ...add $-2$ to each side. $ x+2-2=\pm\sqrt{3}-2\qquad$ ...simplify. $x=-2\pm\sqrt{3}$
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